6

5

買

9

307. The last inversion of a chord of the prepared having the 9th in the bass is unavailable, because it would resolve on the unsatisfactory second inversion of the ensuing chord.

308. The second inversion of every common chord has hitherto been disallowed, because the 4th from the bass is in the diatonic style, a discord; whereas the inverted root is always a concord, and hence the ambiguity of the combination. The second inversion of the tonic chord exceptionally may be used in the exercises now proposed, provided it follow a chord of which the same bass-note is the root; and it thus stands, as might any chord, upon a dominant pedal. The bass-note of the second inversion must either continue under the following chord, or must proceed a 2nd downward or upward when the harmony changes.

309. The Counterpoint to any strain of a melody, which comprises several rythmical periods, may effectively begin with a shorter or longer rest; but in the course of any one strain rests are undesirable in an exercise, since to write them requires no practice.

310. Here is a model in Double Counterpoint in the 8th, on a familiar melody, of Exercises now to be written, wherein the entire class of discords last described, 5ths, 7ths, and 9ths, and also the exceptional second inversion of the tonic concord may be sparingly employed, in addition to the passing-notes and suspensions of earlier use.

311. All the concords produce other concords when inverted a tenth above or below, and all the discords produce other discords when so inverted.

312. The two parts must never be at a greater interval than a 10th (Sect. 287).

313. Here is a table of the intervals and their inversions in the 10th above and below any note with which they may be sounded. Those marked * are only available as discords.

314. Here is a model in Double Counterpoint in the 10th, on the same melody that is given at Sect. 310, of Exercises now to be written.

S

(a) Intelligent students will forgive the admonition that consecutive 10ths or 3rds are unavailable, because their inversion produces 1sts or 8ths; as are consecutive 6ths, because their inversion produces consecutive 5ths.

315. The 6th produces a 7th when inverted a 12th above or below, and is therefore unavailable as a concord,

316. The two parts must never be at a greater interval than a 12th (Sect. 287).

317. Here is a table of the intervals and their inversions in the 12th above and below any note with which they may be sounded. Those marked are only available as discords.

318. Here is a model in Double Counterpoint in the 12th, on the same melody that is given at Sects. 310 and 314, of Exercises now to be written.

(a) The conclusion must be free, in order to obtain a satisfactory cadence; were it otherwise, either the over-counterpoint would end on the 3rd above, or the under-counterpoint on the 3rd below the key-note.

319. This consists of three melodies to be performed at once, each of which is good as the bass, or as the inner part, or as the highest part, and the three may be inverted so as to bring them in these several relations to each other.

(a) The conclusion must be free to prevent the ill effect of the 3rd above the subject proceeding to the bare 5th in the final bar; and this will be the case with all Double Counterpoint in the 12th constructed on a melody which has a satisfactory termination.

320. A complete common chord must never be employed, because its 5th if inverted as a bass would stand as a 4th below the root. The single exception from this necessity is where the 5th

of the tonic chord may exceptionally be used for the bass (Sect. 308). In every other instance, the 5th from the bass is to be treated either as a passing-note,

321. Duplication of the bass-note in the first inversion of a chord is more freely permissible than under other circumstances, since often inevitable where only the root and 3rd, or else the 3rd and 5th of the original chord are available.

322. A leap of the highest part to the 8th of the bass when the bass moves is occasionally admissible, because often unavoidable (Sect. 44).

323. The device may be copiously used of approaching and quitting a discord by contrary motion (Sect. 55), the doubled leading-note may thus be treated as a discord, and so may the combined intervals of the 6th and 4th from the bass; that is, when the discordant notes are approached and quitted by 2nds.

324. Triple Counterpoint may be constructed by adding 3rds above or 6ths below either part of a Double Counterpoint in the 8th; or else by adding 3rds below or 6ths above either part of a Double Counterpoint in the 10th, if the two parts be constructed with a view to such addition.

325. It will often be necessary to invert a part in the interval of the 15th or 17th, instead of the 8th or 10th, and then the directions in Sects. 287 and 312 must be disregarded.

326. A complete composition cannot be written in Triple Counterpoint, because one of the inversions will terminate with the 3rd, instead of the root of a chord in the bass. Therefore, either the final close must be free, or else a passage in Triple Counterpoint can but occur incidentally, to be followed by other matter which will induce a satisfactory termination.